The lumen of the nuclear pore complex is increasingly understood to be lined by a polymer brush that entropically regulates transport in and out of the nucleus—and it seems likely that similar effects probably arise with glycocalyx-lined holes in cell membranes. Here we mimic such pore-confined brushes with self-assembled polymer membranes imbued with nano-holes. Experiment and theory help elucidate the entropic origin and stabilization of the pores, which appear to have a similar basis as steric stabilization of colloids bearing polymer brushes. Free energies of interacting brushes reveal stable minima at pore sizes smaller than the classical metastable point, with little effect of the particular pore geometry. Such entropic forces have potential implications for lock and key mechanisms of nuclear pore assembly as well as transient poration of cells and synthetic nano-pores with regulatory mechanisms for transport.